Consensus formation times in anisotropic societies

We developed a statistical mechanics model to study the emergence of a consensus in societies of adapting, interacting agents constrained by a social rule B. In the mean-field approximation, we find that if the agents' interaction H_{0} is weak, all agents adapt to the social rule B, with which they form a consensus; however, if the interaction is sufficiently strong, a consensus is built against the established status quo. We observed that, after a transient time α_{t}, agents asymptotically approach complete consensus by following a path whereby they neglect their neighbors' opinions on socially neutral issues (i.e., issues for which the society as a whole has no opinion). α_{t} is found to be finite for most values of the interagent interaction H_{0} and temperature T, with the exception of the values H_{0}=1, T→∞, and the region determined by the inequalities β<2 and 2βH_{0}<1+β-sqrt[1+2β-β^{2}], for which consensus, with respect to B, is never reached.